helm/software/matita/contribs/procedural/CoRN/model/structures/Nsec.mma

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  14
  15 (* This file was automatically generated: do not edit *********************)
  16
  17 include "CoRN.ma".
  18
  19 (* $Id: Nsec.v,v 1.6 2004/04/06 15:46:05 lcf Exp $ *)
  20
  21 (*#* printing {#N} $\ensuremath{\mathrel\#_{\mathbb N}}$ *)
  22
  23 include "algebra/CLogic.ma".
  24
  25 (*#* *[nat]
  26 **About [nat]
  27
  28 We prove some basic lemmas of the natural numbers.
  29
  30 A variant of [0_S] from the standard library
  31 *)
  32
  33 inline procedural "cic:/CoRN/model/structures/Nsec/S_O.con" as lemma.
  34
  35 (*#* ***Apartness
  36 *)
  37
  38 inline procedural "cic:/CoRN/model/structures/Nsec/ap_nat.con" as definition.
  39
  40 (* NOTATION
  41 Infix "{#N}" := ap_nat (no associativity, at level 90).
  42 *)
  43
  44 inline procedural "cic:/CoRN/model/structures/Nsec/ap_nat_irreflexive0.con" as lemma.
  45
  46 inline procedural "cic:/CoRN/model/structures/Nsec/ap_nat_symmetric0.con" as lemma.
  47
  48 inline procedural "cic:/CoRN/model/structures/Nsec/ap_nat_cotransitive0.con" as lemma.
  49
  50 inline procedural "cic:/CoRN/model/structures/Nsec/ap_nat_tight0.con" as lemma.
  51
  52 (*#* ***Addition
  53 *)
  54
  55 inline procedural "cic:/CoRN/model/structures/Nsec/plus_strext0.con" as lemma.
  56
  57 (*#* There is no inverse for addition, because every candidate will fail for 2
  58 *)
  59
  60 inline procedural "cic:/CoRN/model/structures/Nsec/no_inverse0.con" as lemma.
  61
  62 (*#* ***Multiplication
  63 *)
  64
  65 inline procedural "cic:/CoRN/model/structures/Nsec/mult_strext0.con" as lemma.
  66